The other answers have shown how diplomacy can be interesting.
But lets assume your question means that it is important to your plot that your characters are diplomats, but that their work as diplomats is not important to your plot, for example because their role as diplomats allows them to easily cross a border or gain access to some place or information or simply gives them a cover story.
This is similar to a character sleeping: its what they have to do, but its not usually interesting from the point of the plot and you wouldn't bore the readers with telling how your character lays down, pulls up the blanket, closes his eyes, starts to drift off listening to the wind, what he dreams about, how he moves in REM phases, how the light changes with the clouds moving across the moon etc. You just briefly state that they sleep, no more.
With everything else, like diplomacy, you can do the same:
After he was done, John went to bed. When he got up in the morning ...
Pete and Paul went to meet the ambassador. When they came out of the embassy ...
You might include the topics discussed, the outcome of the conversation and anything else in such a short summary, or simply have the visit to the ambassador happen between scenes and let your characters discuss the meeting:
"Okay, let's go see the ambassador."
When they came out, Bob and John looked at each other and shrugged. "Well, that was probably the most boring hour in my life."